Problema Solution
the middle angle of a triangle is two more than twice the smallest angle. the largest angle is two more than five times the smallest angle. find all three angles
Answer provided by our tutors
let 'a', 'b' and 'c' represent the angles of the triangle and let a<=b<=c
a + b + c = 180
the middle angle of a triangle is two more than twice the smallest angle:
b = 2 + 2a
the largest angle is two more than five times the smallest angle:
c = 2 + 5a
by solving the system of equations:
a + b + c = 180
b = 2 + 2a
c = 2 + 5a
we find:
a = 22 degrees
b = 46 degrees
c = 122 degrees
click here to see the step by step solution of the system of equations:
the angles are 22, 46 and 122 degrees.